The stock market’s immediate response was to sell off, as traders puzzled over whether it meant the ECB had just cut off Greece. The temporary confusion also came as investors are warily watching the pressure on Greek banks from a large amount of customer withdrawals.

“It sounded like it was more of a technical issue, but it freaked the market out when it first came out. The euro came off its lows as people read the fine print. Greek banks are undercapitalized. The EFSF is going to infuse more capital, and then they can recapitalize,” said Boris Schlossberg of GFT Forex.

Breaking News: Is the ECB Considering a 'Freeze' on Greek Assets?

CNBC's Brian Sullivan has the latest details on a conflicting report the ECB may consider stopping monetary policy operations to some Greek banks.

A later story by a different wire service, Dow Jones, said the European Central Bank confirmed that some Greek banks are now relying on more expensive Emergency Lending Assistance, issued by the Bank of Greece with the permission of the ECB.

Dow Jones quotes the ECB: “Pending the recapitalization of Greek banks that are severely undercapitalized as a result of the recent PSI operation, some of the Greek banks have been moved to Emergency Liquidity Assistance.” The ECB also said when the recapitalization is complete the banks can return to use the conventional monetary policy operations.

The story noted that the Greek banks, after writing off 53 percent of their government bond holdings, have had little equity, and some have had negative equity since March.

The European Financial Stability Fund is releasing bonds to Greece in tranches and has already transferred 25 billion euros in bonds for the recapitalization of banks. Another 18 billion euros is expected from the EFSF shortly.

Hellenic Financial Stability Facility President Panayotis Thomopoulos was quoted by Dow Jones as saying it expects to vote on the disbursal of funds to the banks by Tuesday or Wednesday.